Mathematical model of COVID-19 transmission in the presence of waning immunity

Abstract

We develop a new transmission model of COVID-19 in the presence of waning immunity with isolation and vaccination in humans. The spreading of the disease is determined by the basic reproduction number (ℜ0). Based on mathematical analysis, we found that the non-endemic equilibrium is locally asymptotically stable when ℜ0 < 1 whereas the endemic equilibrium is locally asymptotically stable when ℜ0 > 1. A numerical simulation is used to show the population dynamics. In conclusion, isolation, and vaccination (once it is available) are regarded as effective strategies for eliminating viruses, or at least to suppress the spread of the disease.